Humanoid robots are envisioned to adapt demonstrated motions to diverse real-world conditions while accurately preserving motion patterns. Existing motion prior approaches enable well adaptability with a few motions but often sacrifice imitation accuracy, whereas motion-tracking methods achieve accurate imitation yet require many training motions and a test-time target motion to adapt. To combine their strengths, we introduce AdaMimic, a novel motion tracking algorithm that enables adaptable humanoid control from a single reference motion. To reduce data dependence while ensuring adaptability, our method first creates an augmented dataset by sparsifying the single reference motion into keyframes and applying light editing with minimal physical assumptions. A policy is then initialized by tracking these sparse keyframes to generate dense intermediate motions, and adapters are subsequently trained to adjust tracking speed and refine low-level actions based on the adjustment, enabling flexible time warping that further improves imitation accuracy and adaptability. We validate these significant improvements in our approach in both simulation and the real-world Unitree G1 humanoid robot in multiple tasks across a wide range of adaptation conditions. Videos and code are available at https://taohuang13.github.io/adamimic.github.io/.